110. Giesbertz KJH, Baerends EJ (2010) Aufbau derived from a unified treatment of occupation
numbers in Hartree-Fock, Kohn-Sham, and natural orbital theories with the Karush-KuhnTucker conditions for the inequality constraints n i 1 and n i ! 0. J Comput Chem 132
(19):194108. doi:10.1063/1.3426319
111. Piris M, Ugalde JM (2009) Iterative diagonalization for orbital optimization in natural orbital
functional theory. J Comput Chem 30(13):2078–2086. doi:10.1002/jcc.21225
112. Requist R, Pankratov O (2008) Generalized Kohn-Sham system in one-matrix functional
theory. Phys Rev B 77(23):235121. doi:10.1103/PhysRevB.77.235121
113. Baldsiefen T, Gross EKU (2013) Minimization procedure in reduced density matrix functional theory by means of an effective noninteracting system. Comput Theor Chem 1003
(SI):114–122. doi:10.1016/j.comptc.2012.09.001
114. Talman JD, Shadwick WF (1976) Optimized effective atomic central potential. Phys Rev A
14(1):36–40. doi:10.1103/PhysRevA.14.36
115. Ku ¨mmel S, Kronik L (2008) Orbital-dependent density functionals: theory and applications.
Rev Mod Phys 80(1):3–60. doi:10.1103/RevModPhys.80.3
116. Gidopoulos NI, Lathiotakis NN (2012) Nonanalyticity of the optimized effective potential
with finite basis sets. Phys Rev A 85(5):046502. doi:10.1103/PhysRevA.85.052508
117. Giesbertz KJH (2010) Time-dependent one-body reduced density matrix functional theory;
adiabatic approximations and beyond. Ph.D. thesis, Vrije Universiteit, Amsterdam
118. Appel H (2007) Time-dependent quantum many-body systems: linear response, electronic
transport and reduced density matrices. Ph.D. thesis, Freie Universita ¨t, Berlin
119. Pernal K, Gritsenko O, Baerends EJ (2007) Time-dependent density-matrix-functional theory. Phys Rev A 75(1):012506. doi:10.1103/PhysRevA.75.012506
120. Pernal K, Cioslowski J (2007) Frequency-dependent response properties and excitation
energies from one-electron density matrix functionals. Phys Chem Chem Phys 9(45):5956.
doi:10.1039/b704797e
121. Pernal K, Giesbertz K, Gritsenko O, Baerends EJ (2007) Adiabatic approximation of timedependent density matrix functional response theory. J Chem Phys 127:214101. doi:10.1063/
1.2800016
122. Tozer DJ, Amos RD, Handy NC, Roor BO, Serrano-Andre ´s L (1999) Does density functional
theory contribute to the understanding of excited states of unsaturated organic compounds?
Mol Phys 97(7):859–868
123. Dreuw A, Weisman JL, Head-Gordon M (2003) Long-range charge-transfer excited states in
time-dependent density functional theory require non-local exchange. J Chem Phys 119
(6):2943. doi:10.1063/1.1590951
124. Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange-correlation functional using the
Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393(1–3):51
125. Gritsenko O, Baerends EJ (2004) Asymptotic correction of the exchange-correlation kernel
of time-dependent density functional theory for long-range charge-transfer excitations.
J Chem Phys 121(2):655
126. Neugebauer J, Gritsenko O, Baerends EJ (2006) Assessment of a simple correction for the
long-range charge-transfer problem in time-dependent density-functional theory. J Chem
Phys 124(21):214102
127. Gritsenko O, van Gisbergen SJA, G€ orling A, Baerends EJ (2000) Excitation energies of
dissociating H2: a problematic case for the adiabatic approximation of time-dependent
density functional theory. J Chem Phys 113(19):8478
128. Giesbertz KJH, Baerends EJ (2008) Failure of time-dependent density functional theory for
excited state surfaces in case of homolytic bond dissociation. Chem Phys Lett 461:338.
doi:10.1016/j.cplett.2008.07.018
129. Maitra NT, Zhang F, Cave RJ, Burke K (2004) Double excitations within time-dependent
density functional theory linear response. J Chem Phys 120(13):5932
Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time. . .
181
numbers in Hartree-Fock, Kohn-Sham, and natural orbital theories with the Karush-KuhnTucker conditions for the inequality constraints n i 1 and n i ! 0. J Comput Chem 132
(19):194108. doi:10.1063/1.3426319
111. Piris M, Ugalde JM (2009) Iterative diagonalization for orbital optimization in natural orbital
functional theory. J Comput Chem 30(13):2078–2086. doi:10.1002/jcc.21225
112. Requist R, Pankratov O (2008) Generalized Kohn-Sham system in one-matrix functional
theory. Phys Rev B 77(23):235121. doi:10.1103/PhysRevB.77.235121
113. Baldsiefen T, Gross EKU (2013) Minimization procedure in reduced density matrix functional theory by means of an effective noninteracting system. Comput Theor Chem 1003
(SI):114–122. doi:10.1016/j.comptc.2012.09.001
114. Talman JD, Shadwick WF (1976) Optimized effective atomic central potential. Phys Rev A
14(1):36–40. doi:10.1103/PhysRevA.14.36
115. Ku ¨mmel S, Kronik L (2008) Orbital-dependent density functionals: theory and applications.
Rev Mod Phys 80(1):3–60. doi:10.1103/RevModPhys.80.3
116. Gidopoulos NI, Lathiotakis NN (2012) Nonanalyticity of the optimized effective potential
with finite basis sets. Phys Rev A 85(5):046502. doi:10.1103/PhysRevA.85.052508
117. Giesbertz KJH (2010) Time-dependent one-body reduced density matrix functional theory;
adiabatic approximations and beyond. Ph.D. thesis, Vrije Universiteit, Amsterdam
118. Appel H (2007) Time-dependent quantum many-body systems: linear response, electronic
transport and reduced density matrices. Ph.D. thesis, Freie Universita ¨t, Berlin
119. Pernal K, Gritsenko O, Baerends EJ (2007) Time-dependent density-matrix-functional theory. Phys Rev A 75(1):012506. doi:10.1103/PhysRevA.75.012506
120. Pernal K, Cioslowski J (2007) Frequency-dependent response properties and excitation
energies from one-electron density matrix functionals. Phys Chem Chem Phys 9(45):5956.
doi:10.1039/b704797e
121. Pernal K, Giesbertz K, Gritsenko O, Baerends EJ (2007) Adiabatic approximation of timedependent density matrix functional response theory. J Chem Phys 127:214101. doi:10.1063/
1.2800016
122. Tozer DJ, Amos RD, Handy NC, Roor BO, Serrano-Andre ´s L (1999) Does density functional
theory contribute to the understanding of excited states of unsaturated organic compounds?
Mol Phys 97(7):859–868
123. Dreuw A, Weisman JL, Head-Gordon M (2003) Long-range charge-transfer excited states in
time-dependent density functional theory require non-local exchange. J Chem Phys 119
(6):2943. doi:10.1063/1.1590951
124. Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange-correlation functional using the
Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393(1–3):51
125. Gritsenko O, Baerends EJ (2004) Asymptotic correction of the exchange-correlation kernel
of time-dependent density functional theory for long-range charge-transfer excitations.
J Chem Phys 121(2):655
126. Neugebauer J, Gritsenko O, Baerends EJ (2006) Assessment of a simple correction for the
long-range charge-transfer problem in time-dependent density-functional theory. J Chem
Phys 124(21):214102
127. Gritsenko O, van Gisbergen SJA, G€ orling A, Baerends EJ (2000) Excitation energies of
dissociating H2: a problematic case for the adiabatic approximation of time-dependent
density functional theory. J Chem Phys 113(19):8478
128. Giesbertz KJH, Baerends EJ (2008) Failure of time-dependent density functional theory for
excited state surfaces in case of homolytic bond dissociation. Chem Phys Lett 461:338.
doi:10.1016/j.cplett.2008.07.018
129. Maitra NT, Zhang F, Cave RJ, Burke K (2004) Double excitations within time-dependent
density functional theory linear response. J Chem Phys 120(13):5932
Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time. . .
181